Globally solving Tikhonov regularized total least squares problem
报告题目(Title)：Globally solving Tikhonov regularized total least squares problem
报告人(Speaker)：夏勇，北京航空航天大学
地点(Place)：教八 107
时间(Time)：2019年3月25日13:30-15:30
邀请人(Inviter)：张辉
报告摘要
The well-known total least squares problem with the general Tikhonov regularization can be reformulated as a one-dimensional parametric minimization problem (PM), where each parameterized function evaluation corresponds to solving an n-dimensional trust region subproblem. Under a mild assumption, the parametric function is differentiable and then an efficient bisection method has been proposed for solving (PM) in literature. In the first part, we show that the bisection algorithm can be greatly improved by reducing the initially estimated interval covering the optimal parameter. It is observed that the bisection method cannot guarantee to find the globally optimal solution since the nonconvex (PM) could have a local non-global minimizer. The main contribution of this talk is to propose an efficient branch-and-bound algorithm for globally solving (PM), based on a new underestimation of the parametric function over any given interval using only the information of the parametric function evaluations at the two endpoints. We can show that the new algorithm (BTD Algorithm) returns a global \epsilon-approximation solution in a computational effort of at most O (n^3/\sqrt{\epsilon}) under the same assumption as in the bisection method. The numerical results demonstrate that our new global optimization algorithm performs even much faster than the improved version of the bisection heuristic algorithm. For a special case, the Tikhonov identical regularized total least squares, we propose a more efficient algorithm based on the hidden convexity.
主讲人简介
北京航空航天大学数数学与系统科学学院教授，2018年优秀青年科学基金项目获得者
